SOLUTION: I have two questions that I need help answering? 1.When simplifying the rational expression, (x+8)/(x +2) explain why it is improper to cancel out the x�s. State a general rule fo

Question 422429: I have two questions that I need help answering?
1.When simplifying the rational expression, (x+8)/(x +2) explain why it is improper to cancel out the x�s. State a general rule for canceling factors in a rational expression and give an example of how this rule would be used.
2.How is a rational expression different from a rational equation? Explain, in your own words, the process for solving a rational equation. Why is it important to find the LCD when solving a rational equation? Is it possible to solve a rational equation without finding the LCD? Give an example.

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
1.When simplifying the rational expression, (x+8)/(x +2) explain why is it improper to cancel out the x�s.
The x's are not factors of the numerator or of the denominator; they are terms.
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State a general rule for canceling factors in a rational expression and give an example of how this rule would be used.
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Only factors that are factors of the whole numerator and the whole denominator
may be canceled.
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[x(x+2)]/[2x(x-3)] = (x+2)/[2(x-3)]
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2.How is a rational expression different from a rational equation? Explain, in your own words, the process for solving a rational equation.
The equation contains a rational expression AND an equal sign.
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Why is it important to find the LCD when solving a rational equation?
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Only fractions with the same denominator can be added or subtracted.
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Is it possible to solve a rational equation without finding the LCD? Give an example.
Yes:
Ex: (x+2)/(x-3) = 6
Cross-multiply to get:
x+2 = 6x-18
5x = 20
x = 4
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Cheers,
Stan H.
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